Question

How do you find the amplitude, period and phase shift of `y= -10 cos 2x`?

Answer 1

amplitude = 10 , period`=pi`

Explanation:

The standard form of the cosine function is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=acos(bx+c)+d)color(white)(2/2)|)))`

amplitude = |a| , period `=(2pi)/b`

phase shift `=-c/b" and " d =" vertical shift"`

here a = - 10 , b = 2 , c = 0 , d = 0

Hence amplitude = | -10| = 10 and period `=(2pi)/2=pi`

Since c = d = 0, there is no phase shift or vertical shift.